Up until the point that BCH surpasses BTC in hashpower, and then catches up, I do not need a fully validating node to determine if I’m using BTC or BCH, all I need to do is check accumulated hash power of the last 100 blocks, and see which is greater. At the point BCH does surpass BTC, that is when BCH become Bitcoin. At that point, selling my BTC for BCH also does not require me to run a fully validating node, only the recipient. And then because BCH now has a greater proof of work due to BCH having caught up to BTC, that means its current difficulty algorithm required a greater amount of proof of work, I can track rates of change in the difficulty, and I still don’t need to run a fully validating node.
If I’m using the chain with the most accumulated hash power, that is Bitcoin. I do not care about validation rules. I do not audit the code that I’m running. I do not trust the people writing the code. The only code I care about is SHA-256 implementations, and there are enough examples of that hashing algorithm’s outputs to test if I’m actually running a SHA-256 algorithm without auditing that code, and it turns out that auditing that code is incredibly easy. Putting trust in fully validating node implementations depends on the benevolence and competence of developers. I prefer to rely upon greed.
I do not care about any particular rule of Bitcoin, I care about solving the Byzantine Generals problem, and then relying on that and that alone. If the generals change the validation rules, they are doing it for their own benefit. This happens to coincide with ensuring that enough of an incentive remains to continue the constant increase in hash power, which thereby ensures the ability to rely on nothing but hash power. I can rely upon this because of the adversarial nature of miners incentives when producing hash power.
I do not care if hash power becomes centralized because natural monopolies are unstable at best, and the potential for competition is enough to keep natural monopolies in line.